Definition 2.6 [1]}
The digital Lusternik-Schnirelmann category of a digital image \(X\)  (denoted \(cat_{\kappa }(X)\) ) is defined to be the minimum number \(k\)  for which there is a cover \(\lbrace U_{1}, U_{2}, ..., U_{k}\rbrace \)  of \(X\)  that satisfies each inclusion map from \(U_{i}\)  to \(X\) , for \(i = 1, ..., k\) , is \(\kappa -\) nullhomotopic in \(X\) .

